Lemma 2.3 
(The inverse image theorem [1]})  Let \(\phi : U \subset R^n \rightarrow R^p\)  be \(C^\alpha \)  mapping, where \(\alpha >\text{max}\lbrace 0,n-p\rbrace .\)  Then \(\phi ^{-1}(0)\)  consists of some \((n-p)\) -dimensional \(C^\alpha \)  manifolds.

